Will categorizr (and this plugin) function and produce what they are supposed to when using a CDN to deliver the site? I don’t understand the technical ways this works as they relate to a CDN and caching, etc… And so am wondering if they are compatible technologies.

Shouldn’t be any major issues relative to CloudFlare that I can see off the bat. If the plugin relies on JavaScript at all, the only thing that *might* impact it from CloudFlare would be Rocket Loader (can easily turn off if there is an issue).